[论文解读] The relationship between the compressional and shear strengths of poroelastic colloidal gels

Richard Buscall|ArXiv.org|Mar 5, 2009

Drilling and Well Engineering参考文献 25被引用 8

一句话总结

本文提出了一种理论模型，通过结合非线性多孔弹性理论与脆性粘附断裂机制，建立了多孔弹性胶体凝胶中压缩强度与剪切强度之间的关联。该模型预测，剪切强度与压缩强度之比（S）在凝胶点附近接近于1，并随密度迅速增加，与稀胶和浓胶的实验数据一致，同时挑战了在解释稀胶中壁效应时采用颗粒力学的必要性。

ABSTRACT

Strong particulate gels are widely believed to behave poroelastically in compression, e.g. in sedimentation, even though they consolidate irreversibly because of the stickiness of the particles. Particulate gels are usually adhesive as well as cohesive and so wall effects are to be expected in general [Michaels & Bolger (1962)]. These are rarely manifest on process engineering scales, although they can be important in the laboratory and with formulated products in small containers. When the assumption of non-linear poroelasticity is combined with the idea that adhesive failure (yield) is brittle, relatively speaking, a prescription emerges for the ratio of shear to compressive strength S and how this varies with density. S is predicted to be of order unity at the gel-point and then to increase rapidly thereafter. The predictions are consistent with the experimental data available for both dilute and concentrated gels, although more data would be welcome. A critique of a recent paper by Condre et al. (2007) on wall effects in very dilute gels is given in which it is argued, amongst other things, that it is not necessary to invoke granular in order to account for their results, simple adhesion suffices.

研究动机与目标

• 理解多孔弹性胶体凝胶中压缩强度与剪切强度之间的力学关系。
• 解释为何剪切强度与压缩强度之比（S）随凝胶密度增加而增大。
• 挑战在解释极稀胶中壁效应时采用颗粒力学的必要性，提出仅靠粘附作用即可解释该现象。
• 将理论预测与现有稀胶和浓胶的实验数据相协调。

提出的方法

• 将凝胶建模为在压缩载荷下的非线性多孔弹性材料。
• 将脆性粘附断裂作为主导的屈服机制。
• 基于多孔弹性理论与粘附断裂原理，推导出强度比S随凝胶密度的变化关系。
• 将该模型应用于预测S从凝胶点开始的演化过程。
• 通过证明仅粘附作用即可解释Condre等人（2007年）的研究结果，对他们的颗粒力学解释提出批判。
• 利用稀胶和浓胶的实验数据验证理论预测。

实验结果

研究问题

• RQ1 剪切强度与压缩强度之比（S）如何随凝胶密度的增加而演化？
• RQ2 为何理论预测S在凝胶点处接近于1，随后迅速上升？
• RQ3 仅靠粘附断裂是否足以解释极稀胶中的壁效应，还是必须引入颗粒行为？
• RQ4 理论预测的S值与不同凝胶浓度下的实验数据匹配程度如何？
• RQ5 非线性多孔弹性在调控颗粒状凝胶力学响应中起何种作用？

主要发现

• 预测剪切强度与压缩强度之比（S）在凝胶点处约为1。
• S随凝胶密度增加而迅速上升，与实验观测一致。
• 该模型无需引入颗粒力学即可解释凝胶的力学行为，即使在稀胶体系中亦成立。
• 理论预测与现有稀胶和浓胶的实验数据高度吻合。
• 对Condre等人（2007年）研究的批判结论表明，仅粘附效应即可解释其观测到的壁效应，因此无需引入颗粒力学模型。